In this section, we briefly review two exact compact object solutions [1]}, [2]} of the Horndenski Lagrangian with non-minimal kinetic coupling
\(S=\int dx^4\sqrt{-g}\left\lbrace \frac{\mathcal {R}}{8\pi } - \left[\varepsilon \,g_{\mu \nu }+ \eta \,G_{\mu \nu }\right]\phi ^{,\mu }\phi ^{,\nu }\right\rbrace ~.\) 
